find the zeros of the quadratic polynomial of x2-4 and verify the relationship between zeroes and coefficientsata
Answers
Answer:
Step-by-step explanation:
Let p(x)=x2−4=x2−22=(x−2)(x+2)
∴ p(x)=0
⇒ (x−2)(x+2)=0
⇒ x−2=0 or x+2=0
⇒ x=2 or x=−2
∴ Zeroes of p(x)are 2 and -2.
Now, sum of zeroes =2+(−2)=0=−01=−coefficient ofxcoefficient ofx2
and product of zeroes =(2)(−2)=−4=−41=coefficient termcoefficient ofx2 Hence Verified.
mark brainliest
Given:
A quadratic polynomial x2 - 4.
To find:
The zeroes of the given quadratic polynomial. Also, verify the relationship between zeroes and coefficients.
Solution:
As given, we have a quadratic polynomial
This can be written as
So, the value of the polynomial will be zero, if
Now,
as we know that in a polynomial ax2 + bx + c, the sum of zeroes is
and
product of zeroes
Where a, b and c are coefficients.
Now,
In the given polynomial x2 - 4, a = 1, b = 0 and c = -4.
So,
Also,
the sum of zeroes
Product of zeroes
As
and
Hence, the zeroes of the given quadratic polynomial are -2 and 2.
Also, the relationship between zeroes and coefficients is verified.